Piezoelectric crystal apparatus



Oct. 11, 1949. w. P. MASON 2,484,635

PIEZOEL ECTRIC CRYSTAL APPARATUS Original Filed Aug. 9, 1943 NH4 H2 P04 Z kH P04 I NH4 H2 As 0 I KHZ A! 0 1 l L" YUM X) 1 X (on r) I Z Z ar TENS/0N) FIG. 3

T2 THICKNESS SHEAR //v VEN TOR W F. MASON A r ram/Ev Patented Oct. 11, 1949 UNI TATES PATENT "O-F FICE "2 ,484,635 PIE ZOEL'ECTR'IC CRYSTAL APPARATUS Warr'enP. Mason, West Orange, N. J assignor to Bell Telephone Laboratories, "Incorporated,

New York, N. Y.,a"corporation of NewYork Original application August'll, 19143, siialfno.

497,883. Divided and this applicationDecenibe! '24, 1'945,-Serial'No. 637,127

I 9' Claims. (01. 171- 327) This invention relates "to piezoelectric -crystal apparatus and particularly to thickness shear mode piezoelectric crystal elements comprising crystalline ammonium "dihydrogen phosphate (NHiHzPOi), potassium 'dihydrogen phosphate (KH2PO4), ammonium dihydrogen arsenate (NH4H2ASO4), potassium dihydrogen arsenate (KHzASOi) and isomorphous combinations.

This application is'a division of my copending application for Piezoelectric crystal apparatus, Serial No.*497-;883,-fi1edAugust 9, 1943ynow Patent No. 2,450,010. Suchcrystal elements are useful as electromechanical transducers utilized, for example, in sonic or supersonic projectors, microphones, pick-up devices and detectors. Also, theymay be utilized asfrequency control elements in electric wave filter systems, oscillation generator systems and amplifier systems. Other applications forsuch crystal elements may include harmonic producers, and, in general, any application Where either a resonant or nonresonant piezoelectriccrystal element may be utilized. The non-linear hysteresis loop characteristics of the non-resonant crystal may bemade use of to produce overtones or harmonics therefrom. V I

One ofthe objects of this invention is to provide useful orientations and modes of motion in crystal elements made from crystalline ammonium dihydrogen phosphate, potassium dihydrogen phosphate, ammonium dihydrogen arsenate, potassiumddihydrogen -arsenate and isomorphous combinations. or ii H I M Otherobjects of "this invention are to provide crystal elements comprising dihydrogen phosphate and arsenals substances that may possess useful characteristics, such as large piezoelectric constants, large'vibrational motion, minimum coupling of the'desired mode of motion with undesired "modesof motion therein, and temperature coefiicients of frequency that may'h'ave'th'e relatively lower values. I V u Another object "of this "invention is to 'take advantageof the high piezoelectric activity, the low cost and other advantagesof crystalline amhydrogen phosphate -and arsenate crystals.

Crystal elements of suitable orientation "but from crystalline ammonium dihydrog'en "phosphate/potassium dihydrogen phosphate, potassium dihydrogen arsenate, ammonium dihydrogen arsenate and isomorphous combinations thereof maybe excited in dififerent modes of motion, such as longitudinal length, longitudinal width or longitudinal thicknessmodes of'moeen,

.45 monium dihydroge'nf phosphate and similar "dishear'facemod'esof motion controlled mainly by the width and length major face dimensions, or thickness shear modes of motion controlled main- 1y by the thickness dimension. Also, low frequency-fiexural modes of motion of either the width bending'flex-ure type" or the thickness bending fiexure type may be utilized. The contour or face modes 'ofmotion may be either the face shear modeof motion, "or the "width or-length 'face longitudinalmodes"of*moti0n, as disclosed 'of motion are similar in the general form of their motion to those of-co'rresponding names that are already known in connection with quartz, Rochelle salt, and other known piezoelectric crys tals.

Crystal elements composed of crystalline ammonium dihydrogen phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate, ammonium 'dihydro'gen' arsenate and isomorphous' combinations may have piezoelectric and elastic cbnstants'onmoduli of considerable interest for use inelectromechanical transducers,

filtersystems "and oscillator syste'ms, for ex.. ample. In "accordance with this invention, a

numberof crystal 3 orientations or cuts are pro- 'vided that may he 'utilized for these purposes and-others. The t'y'pes of crystal cuts may be divided into several categories, 'suchas (a)'crystal cuts that have "relatively large piezoelectric 'constantsandherice maybe driven strongly'piezoele'ctrically, (b) crystal cuts 'that have advantageous "elastic -properties, "such that the long-itudinal'face modes of motion therein are free from" coupling to' the faceshear modes of motion therein, and face shear mode crystal elements that "are free from coupling'with other modes ofmotion therein; and (c) crystal cuts that may have the-relatively lower values of temperature coeflicients of frequency.

Crystal elements comprising ammonium dihydrogen phosphate, p'otassium dihydrogen phosphate, ammonium -dihydrogen arsenate, potassium' dihydrogen arsenate and isomorphous combinations also possess I ferroelectric properties such as large dielectric constants, hysteresis loops andnon linearity ofcharge field. relationships b'elow theiir critical or Curie temperatures shear mode or face longitudinal mode crystals, and by adjusting the length and width dimensions relative to the thickness dimension in the case of thickness mode crystals, such as thickness shear mode crystals or thickness longitudinal mode crystals, Also theeflect ofspurious modes in these face mode and thickness mode dihydrogencrystals may be reduced by the use of centrally disposed electrodes partially covering the major faces of the crystals, in the manner of such Y partial electrodes as are now used in connection The ammonium dihydrogen phosphate crystals, I

for example, may have properties somewhat simi-;.

ture which may be of the order of about 180 C.'

or much higher, and also have no water of crystallization and hence will not dehydrate'when operated in air or in vacuum. The temperature coefficients of frequency for certain of theprincipal cuts are roughly of the order of 100 to 300 parts per million per degree centigrade; The dielectric constants decrease slightly with an increase in temperature while the piezoelectric constants relating charge and stress are nearly independent of temperature. Since the ammonium dihydrogen phosphate crystals have the relatively higher values of electromechanical coupling, and are free from water of crystallization which eliminates dehydration in the crystal, and will stand relatively high operating temperatures of the order of 180 C., or more, they are useful as driving elements for all transducer applications, such as projectors and microphones in underwater sound work, for example. Also, this type of crystal may be used as a substitute for quartz frequency control elements in filter and oscillator applications, especially when ;used with temperature control. For the lower'frequency filter applications, the crystal cuts having the relatively lower temperature coefficients of frequency may be used at ordinary temperatures without temperature control.

Although all four of the crystalline dihydrogen substances particularly mentioned herein have relatively large piezoelectric constants and other useful characteristics, the ammonium dihydrogen phosphate crystal elements may be constructed to have the largest values of piezoelectric constants of the four crystalline dihydrogen phosphate and arsenate salts mentioned, and also generally, are relatively more easy to grow in the sizes and shapes that are useful for cutting crystal elements therefrom.

The crystal elements disclosed in this specification may have conductive electrode coatings on their major surfaces of any suitable composition,

shape, and arrangement, such as those already known in connection with quartz, Rochelle'salt and other piezoelectric crystals; and they'may be mounted and electrically connected by any suitable means, such as for example, by pressure type clamping pins or by conductive supporting wires cemented by conductive cement to the crystal coatings at or near the nodal regions, as already known in connection with quartzgRochelle salt and other crystals having similar or corresponding modes of motion.

Spurious modes of motion may be avoided in these crystal elements by a suitable dimensioning of the crystal element, such as by adjusting the thickness dimension thereof relative to the length and width dimensions thereof, in the case of face with quartz crystals, =for example.

For a clearer understanding of the nature of this invention and the additional advantages, features and objectsthereof, reference is made to thefollowing-description taken in connection with the accompanying drawings, in which like reference characters represent like or similar parts-and in which:

Fig. 1 is a perspective view illustrating the prismatic tetragonal-scalenohedral form in which ammonium dihydrog'en phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate, ammonium" dihydrogen arsenate and isomorphous combinations thereof crystallizes, and also illustrating the relation of the prism faces and cap faces 'of such crystalline substances with respect to the mutually perpendicular electric axis -X, mechanical axis Y, and optic axis Z thereof;

Fig. 2 is a perspective" view illustrating the orientation, in terms of the angles 1;), 0 and ill, of a crystal element cut from any of the dihydrogen crystalline substances illustrated in Fig. 1, and may be taken to illustrate the orientation of any dihydrogen salt crystal element disclosed in this specification; and

Figs. 3, 4 and 5 are perspective views illustrating the orientations of several types of thickness shear'mode crystal elements cut from any of the substances ammonium dihydrogen phosphate,

potassium dihydrogen phosphate and corresponding' arsenate crystal "substances, as illustrated in Fig. 1.

This specification follows the conventional terminology as applied to piezoelectric crystalline substances, which employs three mutually perpendicular X, Y and Z axes, as shown in the drawings, to designate an electric axis, a mechanical axis and an optic axis, respectively, of piezoelectric crystalline substances, and which employs three orthogonal axes X, X and Z to designate the directions of the axes of a crystalline piezoelectric body or element that is angularly oriented with respect to such X, Y and Z axes thereof. 7 r r v r This specification also follows the conventional terminology usedto designate the elastic constants s and c, the piezoelectric constants d and other constants of piezoelectric crystalline substances. As an illustrative example, the (Z36 piezoelectric constant means that a Z axis field represented by the numeral 3 may produce XY shear motion represented by the numeral 6. If the d36 piezoelectric constant of the substance has a large value, as it does in thecase of the several dihydrogen salt crystals here considered, then a Z axis fieldapplied thereto may produce a strong shear motion in the XY plane of the crystal body.

The value of the elastic compliance and shear stiffness for rotated crystal elements may be calculated from the fundamental elastic matrix given in Equation 1 in my parent application hereinbefore referred to; One method of doing this is by the short-hand matrix method discussed in a paper The mathematicsof crystal properties, by W. L. Bond, Bell System Technical Journal, January 1943, page 1, using the matrix Where the axes X, Y and Z of the rotated crystals are related to the crystallographic axes X, Y and Z by the direction cosines 21 to m, 11 being the direction cosine between X and X, m the direction cosine between Z and Z, etc. As'shown by Bond, the elastic compliances of rotated crystals are given in terms of the elastic compliances of unrotated crystals by the product of the matrices.

The direction cosines that cause the length dimension L of the crystal element to point in the desired direction are used. For this purpose, the system of angles illustrated inFig. 2 is used where the length L of the crystal is taken along the X axis, the width W is taken along the Y axis and the thickness T is taken along the Z axis. The angle measures the angle between the Z crystallographic axis and the Z thickness T axis. The angle (p measures the angle between the XZ plane and the Z2 plane and 1 1/ the skew angle, is the angle between the length dimension L of the crystal and the tangent to the great circle through the Z and Z areas.

The elastic, dielectric and piezoelectric equations for crystalline ammonium dihydrogen phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate, ammonium dihydrogen arsenate and isomorphous combinations are given in my parent application hereinbefore referred to. These substances crystallize in the prismatic crystal substances crystallize in the prismatic tetragonal scalenohedral form and are formed with four major prism faces and with four cap at each end. The optic axis Z extends beween each apex of the cap faces, and the'mutually perpendicular X and Y axes, extend perpendicular to the four major prism faces. The several cuts or orientations of dihydrogen phosphate and arsenate crystal elements hereinafter disclosed may be cut from the mother crystal I of the substances and form illustrated in Fig. 1.

The mother crystal l illustrated in Fig. 1 may be grown from any suitable substances, and in any suitable manner such as, for example, by'

either the circulation method or the rocking method. As an illustrative example, the potassium salts, used in growing the mother crystal I illustrated in Fig. 1, may be obtained from potassium hydroxide and phosphoric or arsenic acid, and the ammonium salts may be obtained from ammonium carbonate and the corresponding acids. Saturated solutions may be prepared from these salts and the crystal I grown from watery solutions at a gradually decreasing temperture in any suitable manner. The crystal shapeillustrated in Fig. 1 may be varied somewhat to obtain either needle-shaped crystals, or the more compact or short prism form as illustratedin Fig. l. Ammonium dihydrogen phosphate produces short and thick prismatic crystals at room temperature. If liquor is added in excess, all of these salts may be crystallized in short prisms at room temperature. The short thick form of crystal l, as illustrated in Fig. 1, is generally the more convenient form for cutting the various orientations of crystal plates therefrom.

Fig. 2 is a diagram illustrating the system, recently defined by the Institute of Radio Engineers, for specifying the orientation for a piezoelectric crystal element or body 2 in relation to its mutually perpendicular X, Y and Z axes. As shown in Fig. 2, the X axis is taken along the length dimension L of the crystal element 2, the Y axis is taken along the width dimension W of the crystal element 2, and the Z axis is taken along the thickness or thin dimension T of the crystal element 2. The angle 0 is, as shown in Fig. 2, the angle between the optic axis Z and the plate normal or Z axis, and the angle q) is the angle between the +X axis by tension) and the intersection of the plane containing the Z and Z axes with the XY plane, while it is the angle between the length L axis X and the tangent of the great circle containing the Z and Z axes as measured in a plane perpendicular to the Z axis. All angles are positive when measured in a counterclockwise direction. Fig. 2 is applicable to a right-hand crystal, such as quartz, following the crystallographers definition and the earlier Biot convention. The positive X axis is the X axis for which a positive charge develops on a tension stress bein applied thereto.

The crystal element 2 of Fig. 2 may be cut from any of the crystalline phosphate and arsenate substances illustrated in Fig. l, and, by specifying the values for the three angles 0, q: and t of Fig. 2 may generally designate the orientation of any of the several crystal elements disclosed in this specification and illustrated in Figs. 3 to 5 of the drawing.

Suitable conductive electrodes such as the crystal electrodes 3 and 4 of Fig. 2 may be placed on or adjacent to or formed integral with the opposite major faces of any of the crystal plates disclosed herein in order to apply electric field excitation thereto. The crystal electrodes 3 and 4 when formed integral with the surfaces of any of the crystal elements 2 may consist of gold, platinum, aluminum, silver or other suitable conductive material deposited upon the crystal surfaces by evaporation in vacuum, painting, spraying, or by other suitable process. If desired, the crystal element 2 may be electroplated to the desired frequency by nickel plating or otherwise.

The thickness shear mode crystal elements illustrated in Figs. 3 to 5 may be utilized at the relatively high thickness mode frequencies, fundamental or harmonic, to generate high frequency waves in liquids for submarine detection and also may be used as frequency control elements in electric wave filter systems, oscillation generator systems and for other purposes where arelatively high frequency or thickness mode crystal element may be desired.

Figs. 3, 4 and 5 are perspective view of thickness shear mode crystal elements 30, 3| and 32 which may be cut from crystalline ammonium dihydrogen phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate, ammonium dihydrogen arsenate and isomorphous combinations, and made into a plate of substantially rectangular parallelepiped shape with its major faces having a length dimension L and width dimension W which may be of equal dimensions or with one dimension either longer or shorter with respect to the other. The frequency determining mam thicknessor thin dimension-T between'themaj'or faces of the crystal elements 30, 3| and 32ris' perpendicular to the other two dimensions L'a'nd W;wh'ich"may be dimensionally related to the thickness dimension T to remove spurious face mode frequencies from the region of the desired thickness 'mode'frequency. "The thickness shear modes of motion in the piezoelectric crystal elements 30, 3| and32 of Figs; 3, 4 and 5 are similar to the same typeo'f shear'motion that obtains in quartz crystals and may be similarly utilized in filter systems and oscillator systems, for example. The thickness shear modes in the four isomorphic dihydrogen crystalsubstances mentioned hereinbefore are generated by the piezoelectric constants 'dg and dg, a

..The piezoelectric constants that have the larger, values are obtained in the three orientations for the thickness shear mode crystal elements 30, 3| and 32 illustrated in Figs. 3, 4 an d 5. In the crystal elements 30. 3|, 32 of Figs. 3, 4 and 5, the frequency is controlled mainly by the relatively thin thickness dimension T, and the major faces thereof may be of square or rectangular shape as illustrated in Figs. 3, 4 and 5, or of circular or othershape if desired. a

, As illustrated in Fig. 8, the crystal element has one pair of its edges along or nearly along the X axis, the rectangular major faces thereof and the normal Z to the major faces being indined at an angle of 45 degrees or nearly 45 degrees with respect to the Y and Z axes, which corresponds to the orientation angles, expressed in terms of the convention illustrated in Fig. 2, of ;i;:0 degrees, 0:45 degrees and 1.11:0 degrees. a v H The crystal element 3| of Fig. 4 has one edge along or nearly along the Y axis, the rectangular major faces and the normal Z to the major faces being inclined at an angle of 45 degrees or nearly 45 degrees with respect to the X and Z axes, which corresponds to the orientation angles or |P =i9 0f degrees, 6:45 degrees and =0 degrees as' ex-" pressed in terms of the convention illustratedin Fig.2. The crystal element 32 of Fig. 5'has one edge along or nearly along the Z axis, the rectangularf major faces and the normal Z to the major faces being inclined at an angle of 45 degrees or nearly; 45 degrees with respect to the X andY axes, which corresponds to the orientation angles of :;45' degrees, 0:90 degrees and 9:90 degrees as ex pressed in terms of the angles illustrated in Fig; '2.

4 The three thickness shear mode crystal"'ele-'- ments 30, 3| and 32 of Figs. 3, 4 and 5, 1'espec"-" tively, when constructed from crystalline ammo nium dihydrogen phosphate, have frequency con-"'- stants of about 1040, 1040, and 1015, respectively, expressed in kilocycles per second per millimeter" of thickness dimension T, and have temperature co-efiicients of frequency of about 308, 308 and l84, respectively, expressed in parts per million per degree centigrade.

As an illustrative example of the characteristics of thickness shear mode crystals, anammonium' dihydrogen phosphate crystal element 3001' Fig? 3 having its width W or length L along the X axis and having its thickness axis T inclined 45" degrees from'the Z axis and having a length L, a width W and a thickness T of about 1.25, 1.25 and 0.103 centimeters, respectively, has afunda mental thickness shear mode resonant frequencyof about 1010 kilocycles per second and. a"-fre'-* quency constant frof about 1040*kilccycles 'per" 75 is the second perniillimeter of thickness dimentions T for its fundamental thickness shear mode frequency, a shear elastic constant a temperature coefficient of thickness shear mode frequency of about -308 parts per million per degree centlgrade and-a temperature coeflicient of abo ut;;.666 forit-s shear elastic constant .A another illustrative example of the characteristics of a thickness shear mode crystal element,.an ammonium dihydrogen phosphate crystal element 32 of Fig. 5 having its width W or lengthL along the, Z axis and having its thickness axis T ..incline d 45 degrees from the X axis and havinga length L, a width W and a thickness T 0f .ahout, 1 .&48, 1.84.0 and 0.256 centimeters, re-

' sl fitively hasiafundamental resonant frequency Qf.,335,.81 kilo cycles per second and a frequency constant jrof about 1015 kilocycles per second penmillimeter ofthickness T for its fundamental thickness shear mode frequency, a shear elastic :parts-per million per degree centigrade, and a temperature coefficient "of about 388 for its shear elastic constant thickness shear mode crystal element 30 0f,lig..3 having its Width W or length L along the,,X axis and having its thickness axis T inclined at an angle of about 45 degrees from the Y..and.Z. axes, corresponding to angles in Fig. 2 o1,l/ :0.degrees, degrees and 0: 5 degrees, is controlled by the elastic constant:

K viiiit 0 -0 [sin (PH-c [cos 0] :lThe tl'llckness shear mode crystal element 32 of Fig fi having its width W or length L along the z axis and,having its thickness axis T inclined atan angle of,,45 degrees from the X and I axes, corresponding to angles in Fig 2 of 0:90 degrees ,b ='0 degrees and =45 degrees, is contrc lled by the elastic constant and: for all angles of rotation about the Z axis, the thickness 'shear modulus is given by:

, f=ii iH- in 1=i .='Ihe..-thickness-shearmode frequency f of the crystal element 30 of Fig. 3, 3| of Fig. 4 and 32 of Fig. 5 is given by the following equations, re-

T isfthef thickness r in millimeters p is'the' density which in the case of ammonium phosphate is about 1.8

, cf", ci' and of;

corresponding shearing elastic constant.

aesaeae The. thickness; shear mode crystal. elements ;30-, 3i and 32; of Figs, 3, 4 and B-may be adaptedto vibrate alone. or simultaneously. in two thickness shear m des of o n. one. ein the. u amental thickness.shear...mode.and the other the second thickness,S ater.mode,v in. the manner as disclosedin W. P; MasonPatent 2,303,375 dated December 1, 1942. Both thefirst, and, second shear mode frequencies. are controlled mainly by the thickness dimension T of the crystal element and vary inverselyaslthe. valueof the thickness dimension T ofthe.crystalelement. I v

The coupling between the fa e shear, modeo motion and the thickness shearm'ode of motion is controlledby the elasticl'constant The value of for the thickness shear mode crystal elements 3 0 clt= 5 sin which goes to a zero value only at 0:0 degrees and 0:90 degrees where no piezoelectric thickness shear driving constant is present. On the other hand, for the orientation of Fig. 5,

vanishes, and this crystal element 32 of Fig. 5 will have no coupling to a face shear mode of motion.

Although this invention has been described and illustrated in relation to specific arrangements, it is to be understood that it is capable of application in other organizations and is, therefore, not to be limited to th particular embodiments disclosed, but only by the scope of the appended claims and the state of the prior art.

What is claimed is:

1. A piezoelectric crystal element adapted for thickness shear motion at a frequency controlled mainly by its thickness dimension between its major faces, and comprising one of the substances ammonium dihydrogen phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate and ammonium dihydrogen arsenate, said major faces being substantially parallel to one of the three mutually perpendicular X, Y and Z axes and inclined at the bisecting angle of substantially 45 degrees with respect to the other two of said three X, Y and Z axes of said crystal element, said angle being a value corresponding to substantially the largest value of piezoelectric constant in said crystal substance for said thickness shear mode of motion.

2. A piezoelectric crystal element in accordance with claim 1 wherein said major faces are substantially parallel to said Z axis, and said bisecting angle of substantially 45 degrees with respect to said X and Y axes corresponds to a value where said thickness shear motion has substantially no coupling to a face shear mode of motion in said major faces.

3. A piezoelectric crystal element in accordance with claim 1 wherein said major faces are substantially parallel to said Y axis, and said bisecting angle is inclined substantially 45 degrees with respect to said X and Z axes and corresponds to a value where said thickness shear mode of motion has a high electromechanical coupling value.

4. A piezoelectric crystal element adapted for 10 thickness shear motionata frequency controlled mainly. by its thickness. dimension between its major. faces, and comprising one of the substances ammonium dihydrogen phosphate, potassium dihydrogen ,phosphate, potassium dihydrogen arsenate and ammonium dihydrogen arsenate, said majoryfaces being substantially parallel :to one of the three mutually perpendicular X, Y and Z axes and inclinedat the bi-secting angle of substantially. 45 .degrees with respect to the other two of saidlthree X, Y andZaxes of. said crystal element, said angle being a value corresponding to substantially the largest value of. piezoelectric constantin saidcrystal substance for said thickness shear mode of motion, and means comprising electrodes cooperating with said major faces for operating said crystal element in said thicknessshear mode ofmotion.

5.; Piezoelectric crystal apparatus in accordance with claim 4wherein said major faces are substantially parallel to said Y axis, and said bisecting angle is inclined substantially 45 degrees Withrespect :tosaid' X and. Z axes and corresponds to a value where said thickness shear mode of motion has a high electromechanical coupling value, and said one of said substances is ammonium dihydrogen phosphate.

6. A piezoelectric crystal element adapted for thickness shear motion at a frequency controlled mainly by its thickness axis dimension between its major faces, and comprising one of the substances ammonium dihydrogen phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate and ammonium dihydrogen arsenate, said major faces being substantially parallel to the Z axis of the three mutually perpendicular X, Y and Z axes and inclined at the bisecting angle of substantially 45 degrees with respect to the other two X and Y axes of said three X, Y and Z axes of said crystal element, said angle being a value corresponding to substantially the largest value of piezoelectric constant in said crystal substance for said thickness shear mode of motion, and said angle being a value corresponding to a substantially zero value of coupling of said thickness shear motion with the face shear mode of motion in said major faces, said thickness dimension being a value corresponding to the value of said frequency for said thickness shear mode of motion, and means comprising electrodes cooperating with said major faces for operatin said crystal element in said thicknes shear mode of motion.

7. Piezoelectric apparatus in accordance with claim 6 wherein said one of said substances is ammonium dihydrogen phosphate.

8. A piezoelectric crystal element adapted for thickness shear motion at a frequency controlled mainly by its thickness axis dimension between its major faces, and comprising one of the substances ammonium dihydrogen phosphate, potassium dihydrogen phosphate, potassium dihydrogen arsenate and ammoninum dihydrogen arsenate, said major faces being substantially parallel to the Z axis of the three mutually perpendicular X, Y and Z axes and inclined at the bisecting angle of substantially 45 degrees with respect to the other two X and Y axes of said three X, Y and Z axes of said crystal element, said angle being a value corresponding to substantially the largest value of piezoelectric constant in said crystal substance for said thickness shear mode of motion, and said angle being a value corresponding to a substantially zero value of coupling of said thickness shear motion with the face shear 11 mode of motion in'said major faces; said thick ness dimension being avalue corresponding to the value of said frequency for said thickness shear mode of motion.

9. A piezoelectric crystal element adapted for thickness shear motion at a frequency controlled mainly by its thickness axis dimension between its major faces, and comprising one of the substances ammonium dihydrogen phosphate, p0- tassium dihydrogen phosphate, potassium dihydrogen arsenate and ammonium dihydrogen arsenate, said major faces being substantially parallel to the Z axis of the three mutually perpendicular X, Y and Z axes and inclined at the bisecting angle of substantially 45 degrees with respect to the other two'X- and Y axes of said three X, Y and Z axes of said crystal element, said angle being a value corresponding to substantially the largest value of piezoelectric'constant in said crystal substance for said thickness shear mode of motion, and said angle being a value corresponding to a substantially zero value of coupling of said thickness shear motion REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PA'I'ENTS Number Name Date 2,303,375 Mason Dec. 1, 1942 2,373,445 Baerwald Apr. 10, 1945 FOREIGN PATENTS Number Country Date 569,285 Great Britain May 16, 1945 

